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 A053698 a(n) = n^3 + n^2 + n + 1. 31
 1, 4, 15, 40, 85, 156, 259, 400, 585, 820, 1111, 1464, 1885, 2380, 2955, 3616, 4369, 5220, 6175, 7240, 8421, 9724, 11155, 12720, 14425, 16276, 18279, 20440, 22765, 25260, 27931, 30784, 33825, 37060, 40495, 44136, 47989, 52060, 56355, 60880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = 1111 in base n. n^3 + n^2 + n + 1 = (n^2 + 1)*(n + 1), therefore a(n) is never prime. - Alonso del Arte, Apr 22 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = (n^4-1)/(n-1) = A024002(n)/A024000(n) = A002522(n)*(n+1) = A002061(n+1) + A000578(n). G.f.: (1+5*x^2) / (1-x)^4. - Colin Barker, Jan 06 2012 a(n) = -A062158(-n). - Bruno Berselli, Jan 26 2016 a(n) = Sum_{i=0..n} 2*n*(n-i)+1. - Bruno Berselli, Jan 02 2017 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Colin Barker, Jan 02 2017 EXAMPLE a(2) = 15 because 2^3 + 2^2 + 2 + 1 = 8 + 4 + 2 + 1 = 15. a(3) = 40 because 3^3 + 3^2 + 3 + 1 = 27 + 9 + 3 + 1 = 40. a(4) = 85 because 4^3 + 4^2 + 4 + 1 = 64 + 16 + 4 + 1 = 85. From Bruno Berselli, Jan 02 2017: (Start) The terms of the sequence are provided by the row sums of the following triangle (see the seventh formula in the previous section): .   1; .   3,   1; .   9,   5,   1; .  19,  13,   7,   1; .  33,  25,  17,   9,   1; .  51,  41,  31,  21,  11,   1; .  73,  61,  49,  37,  25,  13,  1; .  99,  85,  71,  57,  43,  29, 15,  1; . 129, 113,  97,  81,  65,  49, 33, 17,  1; . 163, 145, 127, 109,  91,  73, 55, 37, 19,  1; . 201, 181, 161, 141, 121, 101, 81, 61, 41, 21, 1; ... Columns from the first to the fifth, respectively: A058331, A001844, A056220 (after -1), A059993, A161532. Also, eighth column is A161549. (End) MAPLE A053698:=n->n^3 + n^2 + n + 1; seq(A053698(n), n=0..50); # Wesley Ivan Hurt, Apr 22 2014 MATHEMATICA Table[n^3 + n^2 + n + 1, {n, 0, 39}] (* Alonso del Arte, Apr 22 2014 *) PROG (MAGMA) [n^3+n^2+n+1: n in [0..50]]; // Vincenzo Librandi, May 01, 2011 (PARI) Vec((1 + 5*x^2) / (1 - x)^4 + O(x^50)) \\ Colin Barker, Jan 02 2017 CROSSREFS Cf. A237627 (subset of semiprimes). Cf. A062158. Sequence in context: A062486 A193226 A291555 * A162867 A059140 A031164 Adjacent sequences:  A053695 A053696 A053697 * A053699 A053700 A053701 KEYWORD nonn,easy AUTHOR Henry Bottomley, Mar 23 2000 STATUS approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)